Why is Information Filter called Information Filter?
I am probably not qualified to answer your question, but I will attempt. At the very least I hope to start a discussion about the matter because I am unsure.

The (linear) Kalman filter uses the error Covariance as it's main contributor to the Kalman gain. We usually notice the Error covariance decreases over time which can be thought of as the decrease in uncertainty. In the information filter the inverse is true. Our "information matrix" increases with more measurements, because our information increases. 

Additionally the measurement update of the information state vector y resembles the way we simply add information. Since 

y(i+1) = y(i) + i(i+1)


here we are simply adding information.

This is how I reason and remember the Information filter. I'm not sure where the name came from.

Additionally:
Arthur Mutambara mentions: "The information filter essentially tracks information about the states and not the states them selves". This may be more correct and concise.